ForHosting KIT · Developer Utilities

Dice expected value and variance

A fair die with a known number of faces is one of the cleanest discrete random variables in probability: each integer from one through the number of sides is equally likely, and independent rolls add without covariance.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

Students, game designers, and analysts often need the expected value and the variance of that experiment—not the chance of a particular total, and not a simulated face. This calculator accepts the number of sides and the number of independent rolls, then returns both statistics for the sum using the closed formulas expected value equals rolls times sides plus one over two, and variance equals rolls times sides squared minus one over twelve. The same pure arithmetic powers the free browser widget and the API, so homework checks and production fixtures never disagree. Failed validation is not billed; a successful call costs $0.002.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/stat/dice

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/stat/dice \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"sides":6,"rolls":1}'

const res = await fetch("https://api.kit.forhosting.com/stat/dice", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "sides": 6,
    "rolls": 1
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/stat/dice",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "sides": 6,
    "rolls": 1
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/stat/dice", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"sides":6,"rolls":1}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"sides":6,"rolls":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/stat/dice", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "sides": 6,
  "rolls": 1
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "stat.dice",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Limits

`max_sides`	1000000
`max_rolls`	1000000

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Read the full KIT documentation →